The distribution and storage of natural gas is based on different pressure levels. The pressure is increased by process gas compressors and currently reduced by throttling valves. The isenthalpic throttling leads to exergy losses. As part of an industry project the TU Dresden and the IME Aachen GmbH developed a bi-directional Wankel machine that may be used for both compression and expansion and thus recover some of the exergy losses. The Wankel machine uses rotary valves for suction and discharge control with fixed opening and closing angles in regards to the displacer rotation. This study shows the detailed design concept of the Wankel machine and the corresponding thermodynamic model, which is based on the compressor calculation software KVA developed at the TU Dresden. The model and its results were used to conduct an in-depth analysis of the machine, including pressures and temperature curves during one displacer rotation, its expected overall efficiencies, occurring exergy losses and its economic potential. The results reveal a considerable energy savings potential for future natural gas storage and distribution application.